Problem: Simplify the following expression and state the condition under which the simplification is valid: $n = \dfrac{p^2 - 4}{p^2 + 2p}$
Explanation: First factor the expressions in the numerator and denominator. $ \dfrac{p^2 - 4}{p^2 + 2p} = \dfrac{(p - 2)(p + 2)}{(p)(p + 2)} $ Notice that the term $(p + 2)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(p + 2)$ gives: $n = \dfrac{p - 2}{p}$ Since we divided by $(p + 2)$, $p \neq -2$. $n = \dfrac{p - 2}{p}; \space p \neq -2$